1. Technical Field
The present invention relates to a method and a device for decoding signals transmitted according to a modulation implementing a constellation.
2. Discussion of the Related Art
An example of a modulation implementing a constellation is the quadrature amplitude modulation, which consists of simultaneously transmitting two amplitude-modulated components having a 90-degree phase shift. A modulated signal Sn, transmitted for a duration T, thus has the following form:S(t)=a*sin(2πft)+b*cos(2πft)  (1)where amplitudes a, b, constant during transmission time T, are selected from among couples of possible values. Each pair (a, b) may be represented in a Cartesian referential by a point P, having its abscissa I, or in-phase component, corresponding to data a, and its ordinate Q, or quadrature component, corresponding to data b. The expression “constellation” corresponds to the representation of all the possible points P for transmission in an orthonormal referential.
According to the coding method used, the number of possible couples (a, b), or number of states nstates, varies. Each point P may be associated with a digital data item containing a number of bits nbits which depends on the allowed number of states nstates according to the following relation:nbits=Int(log2(nstates))  (2)where Int is the whole portion function.
As an example, when nstates is equal to 64, the modulation is called the QAM 64 modulation and nbits is equal to 6. The maximum amplitudes of components I and Q being necessarily bounded, the number of bits nbits of the digital data associated with points P depends on the minimum acceptable distance separating points P of the constellation from one another. In practice, the larger the minimum distance, the more robust the coding process is against noise. The number of bits nbits that can be associated with a QAM symbol thus then essentially depends on the noise level present on the communication channel used for the transmission of signals s.
To each point in the constellation is assigned a label varying from 0 to nstates-1, which corresponds to digital data with nbits bits. Such an operation is called the labeling. The function enabling transforming a digital data item with nbits bits into components I and Q of the associated constellation point is called the mapping function. The choice of the mapping function enables increasing the spectral efficiency, that is, the number of bits transmitted per time unit and per frequency band. A received signal s′ corresponds to a transmitted signal s disturbed by the noise present on the communication channel used for the signal transmission.
The decoding method consists, from the received signal s′, of determining two components Irec and Qrec to place a received point Prec on the representation of the constellation. Due to the noise present on the communication channel, point Prec generally does not exactly correspond to the transmitted constellation point.
A general step of the decoding process called the hard demapping then consists of determining, based on the received point Prec, which is the constellation point, or reference point Pref, corresponding to the transmitted signal with the greatest probability. Such a step consists of determining the constellation point which is closest to received point Prec according to the Euclidian distance. The digital data associated with the reference point is called the reference data.
The sole previous step of the decoding does not enable associating with reference point Pref information relative to the interference which may have affected received signal s′. This is why current decoding methods generally comprise an additional step, called a soft demapping, which consists, for example, of providing for each received signal s′ a decoding data item corresponding to a sequence of signed values, for example of the type (−5; −1.2; 9.2; −0.2). The sign + or − of a signed value at a determined rank in the signed value sequence represents value 0 or 1 of the bit of same rank of the reference data. Each absolute value of a signed value at a determined rank represents information relative to the interference which may have affected the received signal for the bit of same rank of the reference data. The signed values are also called soft bits. Soft bits bring more information than the mere reference data resulting from the hard demapping step. Many decoding methods use the soft bits as an input. It may be iterative processes of turbocode (convolutional and product), soft-Viterbi, low-density parity code type. Such processes are also called soft input soft output or SISO processes.
The determination of a decoding data item thus requires calculation of a signed value for each bit of the reference data. Such a calculation assumes that the communication channel noise is known and can, for example, be modeled by an additive white Gaussian noise (AWGN). The signed value associated with the bit of rank j, called bitj, of the reference data is obtained by ratio LLRj, called Log Likelyhood Ratio, which is expressed as follows:
                              LLR          j                =                  ln          ⁢                                                    P                1                            ⁡                              (                                                      bit                    j                                    =                                      1                    /                                          s                      ′                                                                      )                                                                    P                0                            ⁡                              (                                                      bit                    j                                    =                                      0                    /                                          s                      ′                                                                      )                                                                        (        2        )            where P1(bitj=1/s′) corresponds to the probability for bit bitj of the digital data associated with received signal s′ to be equal to 1, given the received signal s′, and P0(bitj=0/s′) corresponds to the probability for bit bitj of the digital data associated with the received signal s′to be equal to 0, given the received signal s′. Theoretically, the calculations of probabilities P1, P0 must be performed for all constellation points. However, to reduce the calculation time and reduce the complexity of the circuit implementing the calculation (for example, an integrated circuit), a good approximation of ratio LLRj may be obtained by using only two points of the constellation, more specifically the points which bring the greatest contributions to probabilities P1 and P0. For each considered bit of rank j, the constellation point closest to the received point Prec and for which the bit of rank j of the digital data has a value opposite to the bit of same rank of the reference data is called the concurrent point Pconcj. Calling σ2 the variance of the Gaussian noise of the communication channel, considering that probabilities P1 and P0 each follow a normal distribution, ratio LLRj may be expressed as follows:
                                                    LLR            j                                    =                                                                                                                  P                    rec                                    -                                      P                    conc                    j                                                                              2                        -                                                                                                P                    rec                                    -                                      P                    ref                                                                              2                                            2            ⁢                                                  ⁢                          σ              2                                                          (        3        )                                                          ⁢                  =                                                                                                                ⌊                                                                                                    (                                                                                          I                                rec                                                            -                                                              I                                conc                                j                                                                                      )                                                    2                                                +                                                                              (                                                                                          Q                                rec                                                            -                                                              Q                                conc                                j                                                                                      )                                                    2                                                                    ⌋                                        -                                                                                                                    [                                                                                            (                                                                                    I                              rec                                                        -                                                          I                              ref                                                                                )                                                2                                            +                                                                        (                                                                                    Q                              rec                                                        -                                                          Q                              ref                                                                                )                                                2                                                              ]                                                                                      2              ⁢                                                          ⁢                              σ                2                                                                                                                  sign          ⁡                      (                          LLR              j                        )                          =                              2            ⁢                          P              ref              j                                -          1                                    (        4        )            where sign is a function equal to +1 when ratio LLRj is positive and equal to −1 when ratio LLRj is negative, Irec, Iref, and Iconcj are the components I respectively of points Prec, Pref, and Pconcj, and Qrec, Qref, and onc are the components Qconcj of points Prec, Pref, and Pconcj, and Prefj is the value of the bit of rank j of point Pref.
The determining of concurrent point Pconcj for a bit bitj is generally obtained by calculating the distance separating received point Prec from each possible concurrent point Pconcj for which the bit of rank j of the digital data associated with concurrent point Pconcj has a value opposite to the bit of rank j of the reference data, and by choosing the point for which the calculated distance is minimum.
For a given reference point Pref, generally nstates-1 distances are calculated. The determination of the sequence of signed values of the decoding data thus requires a significant calculation time which may have an adverse effect, especially when the decoding process is performed in real time. Further, like for the step of determination of reference point Pref, the steps of determination of concurrent points Pconcj require for coordinates I and Q of all constellation points to be memorized and accessible.